To end this section, let us compare the running (REF ) with
the one in the effective approach to quantum GR with cosmological
constant [1]}I am grateful to Breno
Giacchini and Tibério de Paula Netto for the stimulating
discussions of this issue. (see also earlier work [2]} with
the same result but without effective interpretation). In the
effective approach, the higher derivative terms should be neglected,
but without these terms, the invariants (REF ) cannot be
constructed. The way out is to use the Vilkovisky-DeWitt scheme of
unique effective action, that does not depend of parametrization or
gauge fixing by construction [3]}, [4]}. The
calculations in this case give [2]}
\(&&\Gamma ^{1,\,total}_{div} \,\,=\,\,- \,\frac{\mu ^{n-4}}{\epsilon }\int d^nx \sqrt{-g}\,\Big \lbrace \frac{53}{45}\,E_4 + \frac{121}{60}\,R_{\alpha \beta }^2- \frac{29}{60}\, R^2 + 8\,R\Lambda + 12 \Lambda ^2\Big \rbrace .\nonumber \\\) 
